This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator, which is often derived by employing Gaussian random fields, converges in the mean norm of the reproducing kernel Hilbert space to the conditional expectation and this implies local and uniform convergence of this function estimator. By preselecting the kernel, the problem does not suffer from the curse of dimensionality. The paper analyzes the statistical properties of the estimator. We derive convergence properties and provide a conservative rate of convergence for increasing sample sizes.

翻译：本文探讨重塑功能的回归问题,在随机地点出现超常错误,我们处理复制内核Hilbert空间的问题,事实证明,通常通过使用高山随机字段得出的测算符,在复制内核Hilbert空间的中值规范中,与有条件的预期相趋同,这意味着该函数的测算符在本地和统一的趋同。通过预选内核,问题不受维性诅咒的影响。本文分析了测算符的统计属性。我们得出了趋同特性,并为增加样本大小提供了保守的趋同率。